Abstract
We investigate a design concept for thin tiled plates having exactly one degree of freedom. A tiled plate is realized as a tessellation composed by rigid tiles hinged to each other along the sides. The plate can deform in just one way, that is, into a predetermined surface. The family of tilings we consider, the monohedral hexagonal one, with either convex or concave tiles, is rich enough to include many noteworthy tessellations. Corresponding plates can approximate surfaces with positive, negative, and null Gaussian curvature, and may exhibit an auxetic behavior. The proposed architecture is highly scalable and easily manufacturable, and it can find applications not only for civil and aerospace engineering purposes, but also for biomechanical scaffolds, energy harvesters, and wearable devices.
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References
Bollobas, B.: Filling the plane with congruent convex hexagons without overlapping. Ann. Univ. Sci. Budapest 6, 117–123 (1963). http://annalesm.elte.hu/annales06-1963/Annales_1963_T-VI.pdf
Dang, X., Feng, F., Plucinsky, P., James, R.D., Duan, H., Wang, J.: Inverse design of deployable origami structures that approximate a general surface. Int. J. Solids Struct. 234–235, 111224 (2022). https://doi.org/10.1016/j.ijsolstr.2021.111224
Liu, H., Plucinsky, P., Feng, F., James, R.D.: Origami and materials science. Phil. Trans. R. Soc. A 379(2201), 20200113 (2021). https://doi.org/10.1098/rsta.2020.0113
Liu, K., Tachi, T., Paulino, G.: Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces. Nat. Commun. 10(1), 4238 (2019). https://doi.org/10.1038/s41467-019-11935-x
Marmo, F., Perricone, V., Cutolo, A., Daniela Candia Carnevali, M., Langella, C., Rosati, L.: Flexible sutures reduce bending moments in shells: from the echinoid test to tessellated shell structures. R. Soc. Open Sci. 9(5), 211972 (2022). https://doi.org/10.1098/rsos.211972
Miranda, R., Babilio, E., Singh, N., Santos, F., Fraternali, F.: Mechanics of smart origami sunscreens with energy harvesting ability. Mech. Res. Commun. 105, 103503 (2020). https://doi.org/10.1016/j.mechrescom.2020.103503 ,http://www.sciencedirect.com/science/article/pii/S009364132030032X
Reinhardt, K.: Uber die Zerlegung der Ebene in Polygone. Ph.D. thesis, Universitat Frankfurt am Main (1918). https://gdz.sub.uni-goettingen.de/id/PPN316479497
dos Santos, F.A., Favata, A., Micheletti, A., Paroni, R.: Design of auxetic plates with only one degree of freedom. Extreme Mech. Lett. 42, 101091 (2021). https://doi.org/10.1016/j.eml.2020.101091
dos Santos, F.A., Favata, A., Micheletti, A., Paroni, R., Picchi Scardaoni, M.: Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations (in preparation)
Treml, B., Gillman, A., Buskohl, P., Vaia, R.: Origami mechanologic. Proc. Nat. Acad. Sci. 115, 201805122 (2018). https://doi.org/10.1073/pnas.1805122115
Acnowledgements
FAdS acknowledges the Fundação para a Ciência e a Tecnologia (FCT) in the framework of project UIDB/04625/2020. RP and MPS acknowledge the support from the University of Pisa through the project PRA2022-69 “Advanced modelling of ultra-lightweight materials and structures”. AF acknowledges the support from Sapienza University of Rome through the research project 2022 “Mechanics of thin structures and 2D materials: advanced models and new applications”. AM acknowledges the funding received in the framework of the project “OPTYMA - Optimized tensegrity metamaterials”, grant number E83C22002290005, of the University of Rome Tor Vergata.
The Italian INdAM-GNFM is acknowledged.
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dos Santos, F.A., Favata, A., Micheletti, A., Paroni, R., Scardaoni, M.P. (2024). Tiled Plates with One Degree of Freedom. In: Gabriele, S., Manuello Bertetto, A., Marmo, F., Micheletti, A. (eds) Shell and Spatial Structures. IWSS 2023. Lecture Notes in Civil Engineering, vol 437. Springer, Cham. https://doi.org/10.1007/978-3-031-44328-2_72
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DOI: https://doi.org/10.1007/978-3-031-44328-2_72
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